Some Drawbacks of the Simes Test in the Group Sequential Setting

The Simes test is designed to test a single null hypothesis formed by taking the intersection of multiple null hypotheses using their p-values. In this short note, we explore a novel application of the Simes test for testing a single null hypothesis in a group sequential setting based on the p-values from sequential looks. We refer to this test as the group sequential Simes test (GSST). It turns out, however, that GSST suffers from some drawbacks. The main drawback is that GSST is uniformly less powerful than the reference group sequential test on which it is based. The reason is that the rejection decision of GSST can be based on a test statistic from an earlier stage, which is not a sufficient statistic. This is also a practical drawback. These drawbacks are discussed in this short note.